Police received reports of several incidents from shoppers in the Elmsleigh Centre in Staines on Saturday.
The man has since been released on conditional bail while enquiries continue.
As part of his bail conditions, he is prohibited from entering either the Elmsleigh Centre or the Two Rivers Shopping Centre.
Spelthorne Neighbourhood Sergeant Kelly Orson said: “We understand that reports of this nature may cause concern within our community, and I would like to reassure residents that we take incidents like this very seriously. Officers responded quickly to the report and arrested a man shortly afterwards. Our enquiries remain ongoing to establish the full circumstances of what happened.
“We are particularly keen to hear from anyone who was in the Elmsleigh Centre around midday on Saturday, 4 July, and who may have spoken to, or been approached by, someone claiming to be a police officer.
“If you have any information, no matter how insignificant you think it may be, please contact us.”
Anyone with information is asked to contact us via direct message or through our website, quoting reference PR/45260079713.
If you do not wish to leave your name, please call the independent charity Crimestoppers on 0800 555 111 or visit their website.
